
Puzzle to illustrate the power of compounding
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
26 November 2023
Suppose you are given
the choice of either getting ten million shillings at once today or
start with one shilling and then the amount is doubled every day for the
next 30 days, which would you choose? In the second option, you get one
shilling on the first day, two on the second, four on the third, eight
on the fourth and so on up to the 30th day.
A puzzle similar to
this one has been doing the round on the social media and David Maina
forwarded it to me recently asking whether it is true that the second
option far better than the first. Well, the proof of the pudding is in
the eating.
This is a simple,
albeit tedious, sum to do. The best way to go about it is to draw a
table with three columns and thirty rows. On the first column you enter
the number of days: from 1 all the way to 30. On the second column will
be the amounts received: starting with Sh1, then Sh2, followed by Sh4,
then Sh8… Be sure to have a calculator at hand.
The third column is
for the running totals. Thus, on day 1, the total received is Sh1; on
day 2 it is Sh1 + Sh2 = Sh3; then on the third day it will be Sh3 + Sh4
= Sh4 and so on. If you do the math correctly, you should find that on
the last day, day 30, the amount received will be Sh536,870,912. Yes:
over half a billion shillings!
And this is just the
amount you get on that day; not the running total! When all the amounts
are added up from the first to the last day, it comes to Sh1,073,741,823
– over one billion billings.
This puzzle is good
illustration of the power of compounding as well as the human brain’s
inability to comprehend it. When we hear that something is “doubled
every day”, we imagine that it is increased by two units daily. Thus, in
the above puzzle, we think the progression will go this way: Sh1, Sh2,
Sh4, Sh6, Sh8…Sh60. But, of course, that is not doubling; it is adding
two.
For the same reason,
it doesn’t sound plausible that, when an investment pays 10 per cent per
year (compounded), it will double in vale in slightly over seven years.
The expectation is that the doubling will only come after ten years.

